Noisy 2-design ensembles show a conditional-entropy-governed threshold for distinguishability preservation while post-measured versions collapse exponentially with no protected regime.
Quantum conditional entropies from convex trace functionals
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abstract
We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity results for these functionals, we establish data-processing inequalities and additivity properties for our entropies, demonstrating their operational significance. We further prove completeness under duality, chain rules, and various monotonicity properties for this family. Our proofs draw on tools from complex interpolation theory, multivariate Araki--Lieb and Lieb--Thirring inequalities, variational characterizations of trace functionals, and spectral pinching techniques.
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quant-ph 1years
2026 1verdicts
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Can scrambling protect quantum state distinguishability under noise?
Noisy 2-design ensembles show a conditional-entropy-governed threshold for distinguishability preservation while post-measured versions collapse exponentially with no protected regime.